São Paulo Road Network Analysis

Pedro Borges — pedro.borges@inpe.br

Geospatial network analysis of the road infrastructure in the City of São Paulo. This notebook presents the results of the analysis pipeline, including global network statistics, node/edge-level parameters, and spatial aggregations by OD zone, district, and subprefecture.

import geopandas as gpd
import matplotlib.pyplot as plt
import contextily as ctx
import pandas as pd
import re
from pathlib import Path

plt.rcParams.update({
    "figure.facecolor": "#1a1a2e",
    "axes.facecolor": "#1a1a2e",
    "text.color": "white",
    "axes.labelcolor": "white",
    "xtick.color": "white",
    "ytick.color": "white",
})

DATA_DIR = Path("data/output")
CRS_WEB_MERCATOR = "EPSG:3857"
BASEMAP = ctx.providers.CartoDB.DarkMatter


def plot_choropleth(gdf, column, title, geom_type="polygon",
                    cmap="plasma", figsize=(12, 10), **kwargs):
    """Plot a choropleth map with a dark basemap."""
    fig, ax = plt.subplots(figsize=figsize)

    plot_kwargs = dict(column=column, cmap=cmap, legend=True,
                       legend_kwds={"shrink": 0.6, "label": column})

    if geom_type == "point":
        plot_kwargs.update(markersize=0.1, alpha=0.6)
    elif geom_type == "line":
        plot_kwargs.update(linewidth=0.15)
    else:
        plot_kwargs.update(alpha=0.7, edgecolor="white", linewidth=0.3)

    plot_kwargs.update(kwargs)
    gdf.plot(ax=ax, **plot_kwargs)

    ctx.add_basemap(ax, source=BASEMAP)
    ax.grid(True, alpha=0.3, color="white", linestyle="--")
    ax.set_axis_off()
    ax.set_title(title, fontsize=14, color="white", pad=12)
    plt.tight_layout()
    plt.show()

Global Network Parameters

text = (DATA_DIR / "results.txt").read_text()

params = {}
for line in text.splitlines():
    match = re.match(r"^(.+?):\s+([\d.]+)", line.strip())
    if match:
        params[match.group(1).strip()] = match.group(2)

df_params = pd.DataFrame(
    list(params.items()), columns=["Parameter", "Value"]
)
df_params

	Parameter	Value
0	Number of nodes (N)	122456
1	Number of edges (L)	304027
2	Average degree (<k>)	4.9655
3	Average clustering coefficient (<c>)	0.0596
4	Average Euclidean distance (<l_eucl>)	92.0898
5	Average Manhattan distance (<l_manh>)	117.0374
6	Average physical length (<length>)	96.9404
7	Topological (edges)	114.3566
8	Physical length (m)	23144.3021
9	Euclidean distance (m)	22754.0413
10	Manhattan distance (m)	28499.9732
11	Maximum Euclidean distance (max_l_eucl)	6540.5646
12	Maximum Manhattan distance (max_l_manh)	8611.8547
13	Maximum physical length (max_length)	6833.8703
14	Diameter (D)	357
15	p = 2L / N(N-1)	0.000041
16	k* = p(N-1)	4.9655
17	c* = k*/N	0.000041
18	l* = logN/logk*	7.3107

Node Parameters

• k_i — Node degree: number of edges connected to each node
• b_i — Node betweenness centrality: fraction of shortest paths passing through each node
• c_i — Clustering coefficient: fraction of a node's neighbors that are also neighbors of each other

nodes = gpd.read_file(DATA_DIR / "nodes.gpkg").to_crs(CRS_WEB_MERCATOR)
nodes[["k_i", "c_i", "b_i", "avg_l_i"]].describe()

	k_i	c_i	b_i	avg_l_i
count	122456.000000	122456.000000	122456.000000	122456.000000
mean	4.965490	0.059641	0.001071	95.989565
std	1.709278	0.127200	0.006706	90.543756
min	1.000000	0.000000	0.000000	0.000000
25%	4.000000	0.000000	0.000020	54.346951
50%	6.000000	0.000000	0.000078	82.972008
75%	6.000000	0.000000	0.000329	116.270134
max	11.000000	1.000000	0.202894	6833.870270

plot_choropleth(nodes, "k_i", "Node Degree (k_i)", geom_type="point")
plot_choropleth(nodes, "b_i", "Node Betweenness Centrality (b_i)", geom_type="point")

Edge Parameters

• e_ij — Edge betweenness centrality: fraction of shortest paths passing through each edge

edges = gpd.read_file(DATA_DIR / "edges.gpkg").to_crs(CRS_WEB_MERCATOR)
plot_choropleth(edges, "e_ij", "Edge Betweenness Centrality (e_ij)", geom_type="line")

Aggregated Parameters by OD Zone

zones = gpd.read_file(DATA_DIR / "zone_summary.gpkg").to_crs(CRS_WEB_MERCATOR)
plot_choropleth(zones, "k_i_mean", "Mean Node Degree by OD Zone (k_i_mean)")
plot_choropleth(zones, "c_i_mean", "Mean Clustering Coefficient by OD Zone (c_i_mean)")
plot_choropleth(zones, "b_i_mean", "Mean Node Betweenness by OD Zone (b_i_mean)")
plot_choropleth(zones, "e_ij_mean", "Mean Edge Betweenness by OD Zone (e_ij_mean)")

Aggregated Parameters by District

districts = gpd.read_file(DATA_DIR / "district_summary.gpkg").to_crs(CRS_WEB_MERCATOR)
plot_choropleth(districts, "k_i_mean", "Mean Node Degree by District (k_i_mean)")
plot_choropleth(districts, "c_i_mean", "Mean Clustering Coefficient by District (c_i_mean)")
plot_choropleth(districts, "b_i_mean", "Mean Node Betweenness by District (b_i_mean)")
plot_choropleth(districts, "e_ij_mean", "Mean Edge Betweenness by District (e_ij_mean)")

Aggregated Parameters by Subprefecture

subpref = gpd.read_file(DATA_DIR / "subprefeitura_summary.gpkg").to_crs(CRS_WEB_MERCATOR)
plot_choropleth(subpref, "k_i_mean", "Mean Node Degree by Subprefecture (k_i_mean)")
plot_choropleth(subpref, "c_i_mean", "Mean Clustering Coefficient by Subprefecture (c_i_mean)")
plot_choropleth(subpref, "b_i_mean", "Mean Node Betweenness by Subprefecture (b_i_mean)")
plot_choropleth(subpref, "e_ij_mean", "Mean Edge Betweenness by Subprefecture (e_ij_mean)")